D8fields = [x^8 - 3*x^7 + 4*x^6 - 3*x^5 + 3*x^4 - 3*x^3 + 4*x^2 - 3*x + 1,
x^8 - x^7 + 2*x^6 + 3*x^5 - x^4 + 3*x^3 + 2*x^2 - x + 1,
x^8 - 2*x^7 + 2*x^6 + 2*x^5 - 2*x^4 + 2*x^3 + 2*x^2 - 2*x + 1,
x^8 - 2*x^7 + 2*x^6 - 2*x^5 + 7*x^4 - 10*x^3 + 8*x^2 - 4*x + 1,
x^8 + 6*x^4 + 1,
x^8 - 3*x^7 + 9*x^6 - 13*x^5 + 18*x^4 - 11*x^3 + 11*x^2 - 4*x + 1,
x^8 + 4*x^6 + x^4 - 6*x^2 + 4,
x^8 - 4*x^6 + 8*x^4 - 4*x^2 + 1,
x^8 + 5*x^6 + 4*x^4 + 5*x^2 + 1,
x^8 - 2*x^7 + 2*x^6 + 4*x^5 - x^4 + 4*x^3 + 2*x^2 - 2*x + 1,
x^8 + 3*x^4 + 1,
x^8 + 3*x^4 + 9,
x^8 - 4*x^7 + 8*x^6 - 10*x^5 + 11*x^4 - 10*x^3 + 2*x^2 + 2*x + 1,
x^8 - x^7 + 8*x^6 + 7*x^5 + 19*x^4 + 7*x^3 + 8*x^2 - x + 1,
x^8 - 3*x^7 + x^6 + 6*x^5 + 6*x^4 + 6*x^3 + x^2 - 3*x + 1,
x^8 - 4*x^7 + 8*x^6 - 6*x^5 + 7*x^4 - 10*x^3 + 2*x^2 - 6*x + 9,
x^8 - x^7 + 2*x^6 - 3*x^5 - x^4 + 6*x^3 + 8*x^2 + 8*x + 16,
x^8 - 5*x^6 + 28*x^4 + 15*x^2 + 9,
x^8 + 2*x^6 + 10*x^4 + 2*x^2 + 1,
x^8 - 2*x^7 + 2*x^6 - 6*x^5 + 14*x^4 - 30*x^3 + 50*x^2 - 50*x + 25]

q8fields = [ x^8 + 12*x^6 + 36*x^4 + 36*x^2 + 9,
  x^8 - 12*x^6 + 36*x^4 - 36*x^2 + 9,
  x^8 - x^7 - 34*x^6 + 29*x^5 + 361*x^4 - 305*x^3 - 1090*x^2 + 1345*x - 395, 
  x^8 - 3*x^7 + 22*x^6 - 60*x^5 + 201*x^4 - 450*x^3 + 1528*x^2 - 3069*x + 4561,
  x^8 + 60*x^6 + 900*x^4 + 4500*x^2 + 5625,
  x^8 - 60*x^6 + 900*x^4 - 4500*x^2 + 5625,
  x^8 - x^7 - 47*x^6 + 40*x^5 + 581*x^4 - 220*x^3 - 2038*x^2 - 932*x - 109,
  x^8 + 84*x^6 + 1764*x^4 + 12348*x^2 + 21609,
  x^8 - 84*x^6 + 1764*x^4 - 12348*x^2 + 21609,
  x^8 + 44*x^6 + 308*x^4 + 484*x^2 + 121,
  x^8 - 44*x^6 + 308*x^4 - 484*x^2 + 121,
  x^8 + 60*x^6 + 1170*x^4 + 9000*x^2 + 22500,
  x^8 + 60*x^6 + 810*x^4 + 1800*x^2 + 900,
  x^8 - 60*x^6 + 1170*x^4 - 9000*x^2 + 22500,
  x^8 - 60*x^6 + 810*x^4 - 1800*x^2 + 900,
  x^8 - 3*x^7 - 63*x^6 + 90*x^5 + 1311*x^4 - 20*x^3 - 7702*x^2 - 5524*x - 1009,
  x^8 + 68*x^6 + 986*x^4 + 4624*x^2 + 4624,
  x^8 - 68*x^6 + 986*x^4 - 4624*x^2 + 4624,
  x^8 - 3*x^7 - 67*x^6 - 16*x^5 + 863*x^4 + 1276*x^3 + 392*x^2 - 54*x + 1,
  x^8 - x^7 + 50*x^6 + 71*x^5 + 529*x^4 + 2173*x^3 + 842*x^2 + 5545*x + 17623]
